A composite function can be written as $w\bigl(u(x)\bigr)$, where $u$ and $w$ are basic functions. Is $h(x)=\sin(\sqrt{x})$ a composite function? If so, what are $u$ and $w$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $h$ is composite. $u(x)=\sqrt{x}$ and $w(x)=\sin(x)$. (Choice B) B $h$ is composite. $u(x)=\sin(x)$ and $w(x)=\sqrt{x}$. (Choice C) C $h$ is not a composite function.
Composite and combined functions A composite function is where we make the output from one function, in this case $u$, the input for another function, in this case $w$. We can also combine functions using arithmetic operations, but such a combination is not considered a composite function. The inner function The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function. Here, we have $\sqrt{x}$ inside parentheses. We evaluate this expression first, so $u(x)=\sqrt{x}$ is the inner function. The outer function Then we take the sine of the entire output of $u$. So $w(x)=\sin(x)$ is the outer function. Answer $h$ is composite. $u(x)=\sqrt{x}$ and $w(x)=\sin(x)$. Note that there are other valid ways to decompose $h$, especially into more complicated functions.